A top of a convertible vehicle having a top linkage displaceable between a closed position, in which the top covers a vehicle interior, and a storage position, in which the vehicle interior is open toward the sky, and which has a linkage arrangement on either side of a vertical longitudinal center plane of the top, the linkage arrangement being covered by a headliner when in the closed position. A fabric deflecting element for the headliner is attached to each of the linkage arrangements, the fabric deflecting element moving relative to a roof side rail when the top linkage is being displaced between the closed position and the storage position, an edge of the headliner being attached to the roof side rail. The headliner slides on a fabric contact surface of the fabric deflecting element when the top linkage is being displaced between the storage position and the closed position.